Loosely-Stabilizing Leader Election with Polylogarithmic Convergence Time

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Theoretical Computer Science

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A loosely-stabilizing leader election protocol with polylogarithmic convergence time in the population protocol model is presented in this paper. In the population protocol model, which is a common abstract model of mobile sensor networks, it is known to be impossible to design a self-stabilizing leader election protocol unless the exact number of agents is known a priori. Thus, in our prior work, we introduced concept of loose-stabilization, which is weaker than self-stabilization but has similar advantage in practice. Following this work, several loosely-stabilizing leader election protocols have been given. Loosely-stabilizing leader election guarantees that, starting from an arbitrary configuration, the system reaches a safe configuration with a single leader within a short time, and keeps the unique leader for a long time thereafter. The convergence times of all existing loosely-stabilizing protocols, i.e., the expected times to reach a safe configuration, are polynomial in n where n is the number of nodes, while their holding times, i.e., the expected times to keep the unique leader after reaching a safe configuration, are exponential in n. In this paper, a loosely-stabilizing protocol with polylogarithmic convergence time is presented. Its holding time is not exponential, rather an arbitrarily large polynomial function of n.


Loose-stabilization; Leader election; Population protocols


Computer Sciences



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